Shapes Out Of Shapes

People see shapes everywhere. Our minds deal with any visual experience by forming meaningful patterns, using a system called object recognition. Most of the time, we are not aware of this process. But you can make a game out of recognizing and making shapes and patterns.

Take this squash, for example. It doesn’t look much like squash, does it? It looks more like a duck. Because our minds analyze shapes automatically, we see all sorts of shapes where we don’t even expect them to be: a vegetable becomes an animal.

We recognize a shape by association with a shape we’ve already seen. You can invite your kids to play recognition games with potatoes and squash at the grocery store, or clouds and tree bark at the park. Or if your kid is a night-time person, people have been looking for shapes in the stars for thousands of years! At home, make random doodles, paint blots, or clay blobs and ask, “What Do You See?” Share what you see, when you are the one to catch a shape: “The stem of the squash is perfect for duck’s beak, because both are flattened cones.” Talking helps everybody, kids and adults, to grow their math eyes.

A shape is just a shape until…

But object recognition is only the first step! Take the game to the next level by adding your own details to the image your mind just found. Several teachers call this game “A Shape Is Just A Shape Until…”

This game gives kids more freedom to tweak and customize shapes than “What Do You See?” does. A shape is just a shape until you add more shapes. Then that shape can be anything!

Integrate in style

The two games I’ve described so far are easy and meditative, because human minds automatically recognize objects. Even newborns are good at that. But building totally new objects out of simple parts is much more challenging. Instead of seeing an existing shape, you need to make a new shape in your mind, as you build or draw it. Since people enjoy challenges, many cultures around the world have games and craft traditions for integrating shapes out of shapes.

Have you ever played with tangrams? The Chinese game of tangrams is about making shapes out of seven pieces called tans, without the pieces overlapping. Some shapes are abstract, but others are images of animals, birds, houses, and so on. The traditional collections of shapes are like galleries of impressionist miniatures.

In one version of the tangram game, you are given silhouettes of shapes. You have to reverse-engineer them to figure out how to make the same shape out of the tans. Some shapes are easy to make, others can take hours to figure out.

Another tangram game is to build your own silhouettes out of the seven tans. It doesn’t sound complex, but there are hundreds of different shapes that can be constructed with tans, and thousands of variations. Of course, you don’t have to play by these rules all the time. See what kind of shapes your kids can invent with more than seven pieces, or with overlaps.

If you or your kid are having a bit of trouble replicating knotwork, try using a grid. Grids help with keeping neat the lines, the angles, and the topology of the knots. Thinky Things has a database of instructions for learning how to draw knotwork.

As with tangrams, you can design abstract knots or flowers, animals, and people. One thing is consistent though: no matter the shape of the final product, each finished knot was built out of smaller shapes!

There are many paths to a single destination. How do you make a bird? Sometimes it’s as simple as walking through the supermarket and seeing a tomato that looks like a duck. Or you can go back in time through hundreds of years, to ancient China or Celtic Europe, and make birds out of tangrams or knotwork. Or, if you don’t want to go to the trouble of building a time machine, modern tools such as LEGO and Minecraft are all about making shapes out of shapes.

While learning about shapes out of shapes, your kid will be practicing object recognition, pattern-making, analysis, and synthesis, all of which are used by mathematicians, engineers, and countless other professions. Every time you see a 3D animation, walk across a bridge, or explore an aviary, you are seeing the product of a mind making shapes out of other shapes.

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Marina Mersenne is a student, writer, and autodidact. As a lifetime unschooler, Marina takes part in discussions concerning learning and educational systems. With Moebius Noodles, she hopes to expand on alternative ways of learning and teaching mathematics.